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A boundary multivalued integral “equation” approach to the semipermeability problem

Jaroslav Haslinger, Charalambos C. Baniotopoulos, Panagiotis D. Panagiotopoulos (1993)

Applications of Mathematics

The present paper concerns the problem of the flow through a semipermeable membrane of infinite thickness. The semipermeability boundary conditions are first considered to be monotone; these relations are therefore derived by convex superpotentials being in general nondifferentiable and nonfinite, and lead via a suitable application of the saddlepoint technique to the formulation of a multivalued boundary integral equation. The latter is equivalent to a boundary minimization problem with a small...

A class of time discrete schemes for a phase–field system of Penrose–Fife type

Olaf Klein (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, a phase field system of Penrose–Fife type with non–conserved order parameter is considered. A class of time–discrete schemes for an initial–boundary value problem for this phase–field system is presented. In three space dimensions, convergence is proved and an error estimate linear with respect to the time–step size is derived.

A free boundary stationary magnetohydrodynamic problem in connection with the electromagnetic casting process

Tomasz Roliński (1995)

Annales Polonici Mathematici

We investigate the behaviour of the meniscus of a drop of liquid aluminium in the neighbourhood of a state of equilibrium under the influence of weak electromagnetic forces. The mathematical model comprises both Maxwell and Navier-Stokes equations in 2D. The meniscus is governed by the Young-Laplace equation, the data being the jump of the normal stress. To show the existence and uniqueness of the solution we use the classical implicit function theorem. Moreover, the differentiability of the operator...

A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α.

Luis A. Caffarelli (1987)

Revista Matemática Iberoamericana

This is the first in a series of papers where we intend to show, in several steps, the existence of classical (or as classical as possible) solutions to a general two-phase free-boundary system. We plan to do so by:(a) constructing rather weak generalized solutions of the free-boundary problems,(b) showing that the free boundary of such solutions have nice measure theoretical properties (i.e., finite (n-1)-dimensional Hausdorff measure and the associated differentiability properties),(c) showing...

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